Thursday, September 20, 2012

Physics, Economics, and Hurricane Arguments

I just finished an interview, via Skype, that will eventually be up on the web. One question I was asked was how knowledge of one field feeds into thinking about another. It occurred to me that I had an interesting example, a case where two unrelated fields, both of which I have worked in, showed that two different arguments for a conclusion in a third field were both wrong.

The three fields are physics, economics, and climate science. The conclusion, widely repeated, is that global warming will result in either more frequent or more violent hurricanes, or both. The conclusion may, for all I know, be correct. Two common arguments for it, however, are both wrong.

The first argument is that hurricanes get their energy from heat, so can be expected to be more violent or more frequent if there is more heat to feed them. That sounds plausible—provided you don't know the relevant physics. A hurricane is a heat engine, converting thermal energy to mechanical energy in the form of moving air. A heat engine does not, indeed cannot, simply convert thermal energy to work—one that did that and nothing else, say a ship that ran without fuel on the heat of the ocean, would be what is called a perpetual motion machine of the second kind and is impossible because it violates the second law of thermodynamics.

A heat engine works by taking heat from a high temperature source, turning some of it into work, and dumping the rest into a lower temperature sink. The amount of work it can get out depends not simply on the temperature of the source but on the temperature difference (if my memory from long ago studies is correct, actually the difference in 1/T) between source and sink. So if you warm both source and sink, air and sea in the case of a hurricane, there is no particular reason to expect that more work will be available, hence no particular reason to expect hurricanes to get either more frequent or more violent.

The second argument is empirical. It is claimed—I presume correctly—that on average you get more hurricanes in hot weather. The obvious conclusion is that if earth's climate gets warmer, we will have more (or more powerful) hurricanes. This time it is economics, in particular the history of ideas in economics, that points out the mistake.

Quite a long time ago, William Phillips, an economist from New Zealand, noticed an interesting empirical relation—on average, when inflation was high, unemployment was low. The relation got labeled the "Phillips Curve." The obvious conclusion was that one could hold down unemployment at the cost of tolerating some inflation. A variety of governments tried to implement such policies. Their failure in the U.S. got labeled "stagflation," a situation with both high unemployment and high inflation.

What was wrong with the Phillips Curve was not the empirical evidence but the causal conclusion. What was really going on, as the evidence is now widely interpreted, was that unemployment tended to be low when inflation was higher than people expected. That makes sense on a fairly simple model. If workers underestimate inflation, they will see wage offers as more attractive than they really are and so be more willing to accept them, less willing to wait for a better job, than they would be if they correctly estimated future inflation. If employers underestimate inflation, they will observe high demand for their products at current prices and see that as a reason to hire more workers and expand production.

Times when inflation is high are also, on average, times when it is higher than people expect, giving you the empirical relation Phillips had observed. But if a government tries to exploit the relation by maintaining an inflation rate of (say) five percent a year, after a while people adjust their expectations accordingly and the unemployment rate goes back up. Raise it to ten percent, unemployment falls briefly, people adjust their expectations, and unemployment goes back up again.

The same argument applies in the case of temperature and hurricanes. On average, times when air temperature are higher than normal are also times when the temperature difference between air and sea is larger than normal—the sea, after all, has enormous heat capacity, and so tends to average out short term fluctuations in air temperature. So the observation that hurricanes are more likely in hot weather does not imply that they would be more likely if both sea and air got warmer, as, in a global warming scenario, they do.

None of this implies that global warming does not make hurricanes more frequent or more violent. I have seen empirical claims in both directions—both that hurricanes are and are not increasing—and do not know enough about the field to evaluate them. But it does mean that two apparently persuasive arguments for why we should expect such a relation are wrong.

And in each case, I spotted the error because of my background in a different, in one case entirely unrelated, field.

7 Comments:

"And in each case, I spotted the error because of my background in a different, in one case entirely unrelated, field."

I am not disputing the role of your background in settling on this conclusion (wrt tornadous as a heat engine); but what might have helped as well is that I remarked as much in one of your posts on the subject, which I believe you acknowledged in a subsequent post.

I dont bring that up to be annoying; even if you remembered, i dont expect a citation; the specifics of that exchange are only memorable to me, because it is not every day that I have the honor of giving a leg up to one of my intellectual heroes.

On a related note: In my mind, I remember that argument as one I came up with independently. But I have several times caught myself holding such beliefs, only to come across my supposedly original thoughts in placed I had known to have visited before. For some reason these are some of my more stinging memories; partially because prior to these realizations, I would have sworn they were original thoughts. But it is more likely I had skimmed them before, considered them of minor importance, and shelved them somewhere in my subconcious, only to later reappear 'out of nowhere'. I always try to be very carefull about remembering why I think I know something, but that only works so well as your memory does.

But to get back on topic; there may not be such a thing as a truely original idea; but if someone mutters something under his breath, did a tree really fall in the forest? Being able to connect the dots across disciplines, and presenting that in a lucid way, is in my opinion what makes or breaks a good idea.

In re the heat engine argument, the heat in a hurricane is mostly moved by way of water vapor. The vapor pressure of water increases by about 10% for every 3 degrees Fahrenheit or so; if you increase the temperature of the whole system by 3 degrees Fahrenheit, you're likely to increase the power of the hurricane by 10%, not because there's more thermal energy around but because there is a greater capacity to carry it from one place to another.

dWj: That is indeed true; warmer air is a more effective working fluid, which argues in the direction of more huricane energy at higher temperatures. There are a great many nuances of that kind to be made though; CO2 warming shoud happen most strongly some height in the athmosphere, which is where a tornado sinks it heat. What all these factors add up to is not a simple matter

Overall, global warming due to any cause happens rather disproportionally at the poles, which I suppose is due to the fourth-order character of thermal radiation. That does not mean a warmer world is necessarily a less stormy one, but reasoning of this kind seems more robust to me than trying to fish for correlations in a few decades of noisy data, where it is not at all clear if the variable you are looking at (seasonal temperature fluctuations) has an even qualitatively similar effect to the variable one tries to make predictions about (mean global temperatures)

1. Do you remember which post you commented on? Googling around, I seem to have made the point at least as early as March of 2007.

2. One of my (published) ideas was stolen by Ronald Coase--I think a couple of decades before I had and published it. Not even one of Coase's more important contributions. Part of the argument of my first published economics article was anticipated in a book by Trout Rader that I hadn't read.

my feeling is that knowing even a drop of physics or math has helped me immensely in my studies of kabalah and Talmud. It has helped me in understanding the opinion of rabainu tam about sunset.[i had to go through many calculations of the mil] it has also helped to see when sources like rebbi nachman was being misquoted. and has given me the ability to see often when someone talking about some idea in spiritual matters and then tries to relate it to some physical principle is not really well verses in that physical principle.--like the example you are discussing

It must certainly have been before 2008, since I remember being a student still. It could have been much earlier too, since I have been a longtime follower of your blog. The lack of search function has withheld me sofar from trying to dig it up; not sure what handles ive been posting under, nor do I remember specific words used. Who knows, maybe I dreamt the whole thing :). Now I kindof want to know for sure; perhaps ill have time tonight.

just to add something, on one of your refuted arguments, on an increased average temperature not increasing the number of hurricanes due to it creating a perpetual motion machine of the second kind, you are assuming the heat dump is the ocean. it is not. it is the upper atmosphere(the layer sandwiched between the layer being bombarded by solar wind and the thicker lower atmosphere that retains heat. this layer of atmosphere is VERY cold, and is why we get icing on high altitude planes, alond with the decrease in pressure of course).a quick google search brought up this link which describes ithttp://www.srh.noaa.gov/jetstream/tropics/tc.htm